Difference between revisions of "Unit vectors"
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|Title=Determination of the unit vector to a given vector | |Title=Determination of the unit vector to a given vector | ||
|Contents= | |Contents= | ||
− | The vector <math>\vec{\mathbf{b}}</math> is given and the corresponding unit vector shall be determined: | + | The vector <math>\vec{\mathbf{b}}</math> is given and the corresponding unit vector shall be determined: |
:<math> | :<math> | ||
\vec{\mathbf{b}}=\begin{bmatrix} 3\\ 0\\ 4 \end{bmatrix} | \vec{\mathbf{b}}=\begin{bmatrix} 3\\ 0\\ 4 \end{bmatrix} |
Revision as of 16:11, 14 May 2014
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A unit vector is a vector with magnitude 1. The unit vector to a given vector can be determinde by dividing the given vector by its magnitude :
The vector has the magnitude 1 (so ) and is pointed to the direction of . So every vector can be described by its magnitude (so a scalar value) and the corresponding unit vector. Therefore can also be written as follows:
Example: Determination of the unit vector to a given vector
The vector is given and the corresponding unit vector shall be determined: The calculation of the magnitude shows thats it equals 1 indeed: |